The masses and radii of the Earth and the Moon are M1,R1andM2,R2 respectively. Their centres are at a distance d apart. The minimum speed with which a particel of mass m should be projected from a point midway between the two centres so as to escape to infinity is ........

Question

The masses and radii of the Earth and the Moon are M1​,R1​andM2​,R2​ respectively. Their centres are at a distance d apart. The minimum speed with which a particel of mass m should be projected from a point midway between the two centres so as to escape to infinity is ........

Filo · Accepted Answer

Answer: A::B::DSolution: Increases in P.E. of system

= {(P . E .)_{i} - (P . E .)_{f}}

= - {\frac{\frac{G M _{1} M ^{2}}{d} - ( G M ) _{1} m}{d / 2} - \frac{G M _{2} m}{d / 2}] - [- (G M) 2 m (/ (d)]}

= \frac{G m}{d / 2} (w M_{1} + M_{2})

This increase in P.E. is at the expense of K.E. of mass m

∴ \frac{1}{2} m v^{2} =) G m \frac{)}{d / 2} (M_{1} + M_{2})

Where v is the velocity with which mass m is projected

\Rightarrow v = \frac{4 G}{d} (M_{1} + M_{2})

Question Text	The masses and radii of the Earth and the Moon are $M_{1}, R_{1} and M_{2}, R_{2}$ respectively. Their centres are at a distance d apart. The minimum speed with which a particel of mass m should be projected from a point midway between the two centres so as to escape to infinity is ........
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The masses and radii of the Earth and the Moon are $M_{1}, R_{1} and M_{2}, R_{2}$ respectively. Their centres are at a distance d apart. The minimum speed with which a particel of mass m should be projected from a point midway between the two centres so as to escape to infinity is ........

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Practice questions from similar books

The masses and radii of the Earth and the Moon are M1​,R1​andM2​,R2​ respectively. Their centres are at a distance d apart. The minimum speed with which a particel of mass m should be projected from a point midway between the two centres so as to escape to infinity is ........

Text solutionVerified

Practice questions from similar books

The masses and radii of the Earth and the Moon are $M_{1}, R_{1} and M_{2}, R_{2}$ respectively. Their centres are at a distance d apart. The minimum speed with which a particel of mass m should be projected from a point midway between the two centres so as to escape to infinity is ........